299 research outputs found
Moderate deviations for the spectral measure of certain random matrices
We derive a moderate deviations principle for matrices of the form XN = DN + WN where WN are Wigner matrices and DN is a sequence of deterministic matrices whose spectral measures converge in a strong sense to a limit µD. Our techniques are based on a dynamical approach introduced by Cabanal-Duvillard and Guionnet
A Note on Conditional Exponential Moments and Onsager-Machlup Functionals
It is proven that, for any deterministic L2[0,1] function Ï•(t),
E(exp∫10ϕ(t)dwt ∣ ∥w∥ \u3c ε)→ 1 as ε → 0,
where wt is a standard Brownian motion and ∥⋅∥ is any reasonable norm on C0[0,1]. Applications to the computation of Onsager-Machlup functionals are pointed out
Random walks in a random environment on a strip: a renormalization group approach
We present a real space renormalization group scheme for the problem of
random walks in a random environment on a strip, which includes one-dimensional
random walk in random environment with bounded non-nearest-neighbor jumps. We
show that the model renormalizes to an effective one-dimensional random walk
problem with nearest-neighbor jumps and conclude that Sinai scaling is valid in
the recurrent case, while in the sub-linear transient phase, the displacement
grows as a power of the time.Comment: 9 page
Quenched invariance principle for random walks in balanced random environment
We consider random walks in a balanced random environment in ,
. We first prove an invariance principle (for ) and the
transience of the random walks when (recurrence when ) in an
ergodic environment which is not uniformly elliptic but satisfies certain
moment condition. Then, using percolation arguments, we show that under mere
ellipticity, the above results hold for random walks in i.i.d. balanced
environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo
(in journal version) corrected in (26
Anomalous diffusion in disordered multi-channel systems
We study diffusion of a particle in a system composed of K parallel channels,
where the transition rates within the channels are quenched random variables
whereas the inter-channel transition rate v is homogeneous. A variant of the
strong disorder renormalization group method and Monte Carlo simulations are
used. Generally, we observe anomalous diffusion, where the average distance
travelled by the particle, []_{av}, has a power-law time-dependence
[]_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1.
In the presence of left-right symmetry of the distribution of random rates, the
recurrent point of the multi-channel system is independent of K, and the
diffusion exponent is found to increase with K and decrease with v. In the
absence of this symmetry, the recurrent point may be shifted with K and the
current can be reversed by varying the lane change rate v.Comment: 16 pages, 7 figure
Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher
We consider large deviations for nearest-neighbor random walk in a uniformly
elliptic i.i.d. environment. It is easy to see that the quenched and the
averaged rate functions are not identically equal. When the dimension is at
least four and Sznitman's transience condition (T) is satisfied, we prove that
these rate functions are finite and equal on a closed set whose interior
contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title
of the paper. To appear in Probability Theory and Related Fields
Alternative proof for the localization of Sinai's walk
We give an alternative proof of the localization of Sinai's random walk in
random environment under weaker hypothesis than the ones used by Sinai.
Moreover we give estimates that are stronger than the one of Sinai on the
localization neighborhood and on the probability for the random walk to stay
inside this neighborhood
Pharmaceutical induction of ApoE secretion by multipotent mesenchymal stromal cells (MSCs)
<p>Abstract</p> <p>Background</p> <p>Apolipoprotein E (ApoE) is a molecular scavenger in the blood and brain. Aberrant function of the molecule causes formation of protein and lipid deposits or "plaques" that characterize Alzheimer's disease (AD) and atherosclerosis. There are three human isoforms of ApoE designated ε2, ε3, and ε4. Each isoform differentially affects the structure and function of the protein and thus the development of disease. Homozygosity for ApoE ε4 is associated with atherosclerosis and Alzheimer's disease whereas ApoE ε2 and ε3 tend to be protective. Furthermore, the ε2 form may cause forms of hyperlipoproteinemia. Therefore, introduction of ApoE ε3 may be beneficial to patients that are susceptible to or suffering from these diseases. Mesenchymal stem cells or multipotent mesenchymal stromal cells (MSCs) are adult progenitor cells found in numerous tissues. They are easily expanded in culture and engraft into host tissues when administered appropriately. Furthermore, MSCs are immunosuppressive and have been reported to engraft as allogeneic transplants. In our previous study, mouse MSCs (mMSCs) were implanted into the brains of ApoE null mice, resulting in production of small amounts of ApoE in the brain and attenuation of cognitive deficits. Therefore human MSCs (hMSCs) are a promising vector for the administration of ApoE ε3 in humans.</p> <p>Results</p> <p>Unlike mMSCs, hMSCs were found not to express ApoE in culture; therefore a molecular screen was performed for compounds that induce expression. PPARγ agonists, neural stem cell conditioned medium, osteo-inductive media, dexamethasone, and adipo-inductive media (AIM) were tested. Of the conditions tested, only AIM or dexamethasone induced sustained secretion of ApoE in MSCs and the duration of secretion was only limited by the length of time MSCs could be sustained in culture. Upon withdrawal of the inductive stimuli, the ApoE secretion persisted for a further 14 days.</p> <p>Conclusion</p> <p>The data demonstrated that pre-treatment and perhaps co-administration of MSCs homozygous for ApoE ε3 and dexamethasone may represent a novel therapy for severe instances of AD, atherosclerosis and other ApoE-related diseases.</p
Maximum Likelihood Estimator for Hidden Markov Models in continuous time
The paper studies large sample asymptotic properties of the Maximum
Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain,
observed in white noise. Using the method of weak convergence of likelihoods
due to I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and
convergence of moments are established for MLE under certain strong ergodicity
conditions of the chain.Comment: Warning: due to a flaw in the publishing process, some of the
references in the published version of the article are confuse
Increased Seizure Susceptibility in Mice 30 Days after Fluid Percussion Injury
Traumatic brain injury (TBI) has been reported to increase seizure susceptibility and also contribute to the development of epilepsy. However, the mechanistic basis of the development of increased seizure susceptibility and epilepsy is not clear. Though there is substantial work done using rats, data are lacking regarding the use of mice in the fluid percussion injury (FPI) model. It is unclear if mice, like rats, will experience increased seizure susceptibility following FPI. The availability of a mouse model of increased seizure susceptibility after FPI would provide a basis for the use of genetically modified mice to study mechanism(s) of the development of post-traumatic epilepsy. Therefore, this study was designed to test the hypothesis that, mice subjected to a FPI develop increased seizure susceptibility to a subconvulsive dose of the chemoconvulsant, pentylenetetrazole (PTZ). Three groups of mice were used: FPI, sham, and naïve controls. On day 30 after FPI, mice from the three groups were injected with PTZ. The results showed that FPI mice exhibited an increased severity, frequency, and duration of seizures in response to PTZ injection compared with the sham and naïve control groups. Histopathological assessment was used to characterize the injury at 1, 3, 7, and 30 days after FPI. The results show that mice subjected to the FPI had a pronounced lesion and glial response that was centered at the FPI focus and peaked at 3 days. By 30 days, only minimal evidence of a lesion is observed, although there is evidence of a chronic glial response. These data are the first to demonstrate an early increase in seizure susceptibility following FPI in mice. Therefore, future studies can incorporate transgenic mice into this model to further elucidate mechanisms of TBI-induced increases in seizure susceptibility
- …